作者wickeday (WickeDay)
看板Math
标题Re: [代数] p-subgroup的问题
时间Thu May 19 02:00:06 2011
※ 引述《e04su3 (发Q)》之铭言：
: if N normal in G
: N, G/N皆为 p-group
: 证明G is p-group
: 似乎要注意G可能是无限的情形
For any g in G, g+N in G/N
G/N is a p-group => (g+N)^(p^n)=0 for some n
i.e. g^(p^n)=h in N
N is a p-group => h^(p^m)=0 for some m
Hence h^(p^m)=(g^(p^n))^(p^m)=g^(p^(n+m))=0
=> G is a p-group.
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